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Simplifying -7x2 + 42x + 30 = 0 Reorder the terms: 30 + 42x + -7x2 = 0 Solving 30 + 42x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -4.285714286 + -6x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -6x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -6x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -6x + x2 = 0 + 4.285714286 -6x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -6x + x2 = 4.285714286 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 4.285714286 + 9 Reorder the terms: 9 + -6x + x2 = 4.285714286 + 9 Combine like terms: 4.285714286 + 9 = 13.285714286 9 + -6x + x2 = 13.285714286 Factor a perfect square on the left side: (x + -3)(x + -3) = 13.285714286 Calculate the square root of the right side: 3.644957378 Break this problem into two subproblems by setting (x + -3) equal to 3.644957378 and -3.644957378.Subproblem 1
x + -3 = 3.644957378 Simplifying x + -3 = 3.644957378 Reorder the terms: -3 + x = 3.644957378 Solving -3 + x = 3.644957378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.644957378 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.644957378 + 3 x = 3.644957378 + 3 Combine like terms: 3.644957378 + 3 = 6.644957378 x = 6.644957378 Simplifying x = 6.644957378Subproblem 2
x + -3 = -3.644957378 Simplifying x + -3 = -3.644957378 Reorder the terms: -3 + x = -3.644957378 Solving -3 + x = -3.644957378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.644957378 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.644957378 + 3 x = -3.644957378 + 3 Combine like terms: -3.644957378 + 3 = -0.644957378 x = -0.644957378 Simplifying x = -0.644957378Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.644957378, -0.644957378}
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